Calibration of a mechanical property of SPM cantilevers

Abstract

A method is presented for calibrating a cantilever, such as a scanning probe microscope cantilever (SPM cantilever). The cantilever to be calibrated comprises at least a first and a second layer having a mutually different thermal expansion coefficient, the method comprising the steps of: controllably causing a temperature distribution along the cantilever, measuring a spatial state of the cantilever, computing a mechanical property from the observed spatial state caused by controllably changing the temperature. Also a calibration arrangement and a scanning probe microscope provided with the calibration arrangement are presented.

What is claimed is: 
     
       1. An arrangement for calibrating a cantilever, the cantilever comprising at least a first and a second layer having mutually different thermal expansion coefficients, the arrangement comprising:
 a temperature control facility configured to controllably cause a temperature distribution along the cantilever, 
 a measuring facility configured to measure a resulting spatial state of the cantilever, and 
 a computation facility configured to compute a mechanical property from the resulting spatial state corresponding to said caused temperature distribution, 
 
       wherein said measuring facility comprises a first facility configured to measure a deflection or a radius of curvature of the cantilever, and a second facility configured to measure a resonance frequency of the cantilever, and wherein the computation facility is configured to use the measured resonance frequency as well as the measured deflection or radius of curvature to compute the mechanical property. 
     
     
       2. An arrangement according to  claim 1 , wherein said measuring facility includes a first facility is an optical sensor configured to sense a beam reflected by the radiation source. 
     
     
       3. An arrangement according to  claim 1 , wherein the first facility is an optical sensor configured to sense a beam reflected by the radiation source, and wherein the second facility comprises an excitation element configured to cause resonation of the cantilever and an analyzer coupled to an output of the first facility configured to determine a frequency with which the cantilever resonates. 
     
     
       4. A scanning probe microscope comprising an arrangement according to  claim 1 , the microscope further comprising an anchoring facility configured to anchor the cantilever at a first end, an actuator facility configured to controllably position the anchoring facility, the computation facility configured to operate in a mode selected from at least the group consisting of a first, calibration mode, and a second, normal operational mode. 
     
     
       5. A method for calibrating a cantilever, the cantilever comprising at least a first and a second layer having mutually different thermal expansion coefficients, the method comprising the steps of:
 controllably causing a temperature distribution along the cantilever, 
 measuring a spatial state of the cantilever, 
 measuring a resonance frequency of the cantilever, and 
 computing a mechanical property from the measured resonance frequency as well as a measured deflection or radius of curvature caused by controllably changing the temperature. 
 
     
     
       6. The method according to  claim 5 , wherein the step of controllably causing a temperature distribution is performed by controllably heating the cantilever with a photon radiation source. 
     
     
       7. The method according to  claim 5 , wherein the step of controllably causing a temperature distribution is performed by changing an ambient temperature. 
     
     
       8. The method according to claim, comprising the steps of:
 determining in a simulation, for a predetermined amount of heat power (P) supplied to the cantilever and for a predetermined ambient temperature (Ta) value, a first empirical relation between the curvature (κ) or deflection (δ) of the cantilever, its equivalent conductance (G) and its spring constant, k 
 applying said predetermined amount of heat power (P) to a cantilever to be calibrated while maintaining said ambient temperature (Ta) at the predetermined ambient temperature (Ta) value, 
 detecting a resulting curvature (κ) or deflection (δ) of the cantilever, and 
 determining the spring constant (k), from said detected curvature (κ) or deflection (δ) and the equivalent conductance (G) using the first empirical relation. 
 
     
     
       9. The method according to claim, comprising the steps of:
 determining in a simulation, for a predetermined amount of heat power (P) supplied to the cantilever and for a predetermined ambient temperature (Ta) value, a second empirical relation between the a resonance frequency (f) of the cantilever, its equivalent conductance (G) and its spring constant (k), 
 applying said predetermined amount of heat power (P) to a cantilever to be calibrated while maintaining said ambient temperature (Ta) at the predetermined ambient temperature (Ta) value, 
 detecting a resulting resonance frequency (f) of the cantilever, and 
 determining the spring constant, from said detected resonance frequency (f) and the equivalent conductance (G) using the second empirical relation. 
 
     
     
       10. The method according to claim, comprising the steps of:
 applying an initial temperature distribution to a cantilever to be calibrated, 
 allowing an equilibrium temperature distribution to settle, 
 measuring the temperature distribution along the cantilever as a function of time, and 
 calculating a density from the measured temperature distribution along the cantilever as a function of time. 
 
     
     
       11. The method according to claim, comprising determining an equivalent density ρ from a measured thermal diffusivity of a cantilever beam.